Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the \(\ell _1\)-norm regularized minimization problem.

为了解决凸约束非线性方程问题（CCP），已经进行了许多研究以发展和改进迭代方法。基于投影技术，我们引入了一种无导数方法来逼近CCP解。所提出的方法由于其较低的存储要求而适合于求解大型非线性方程。该方法在每次迭代中生成的方向是有界的。在某些温和条件下，我们建立了该方法的全局收敛性结果。数值实验表明了该方法求解CCP的有效性。此外，我们测试了该方法在求解等效于\（\ ell _1 \）-范数正则化最小化问题的单调非线性算子方程中的能力。